In a set of data, the quartiles are the values that divide the data into four equal parts. The median of a set of data separates the set in half.

The median of the lower half of a set of data is the lower quartile ($\text{L}\text{Q}$) or ${Q}_{1}$.

The median of the upper half of a set of data is the upper quartile ($\text{U}\text{Q}$) or ${Q}_{3}$.

The upper and lower quartiles can be used to find another measure of variation call the interquartile range.

The **interquartile range ** or $\text{IQR}$
is the range of the middle half of a set of data. It is the difference between the upper quartile and the lower quartile.

Interquartile range = ${Q}_{3}-{Q}_{1}$

In the above example, the lower quartile is $52$ and the upper quartile is $58$.

The interquartile range is $58-52$ or $6$.

Data that is more than $1.5$ times the value of the interquartile range beyond the quartiles are called outliers.

Statisticians sometimes also use the terms **semi-interquartile range **and **mid-quartile range**.

The semi-interquartile range is one-half the difference between the first and third quartiles. It is half the distance needed to cover half the scores. The semi-interquartile range is affected very little by extreme scores. This makes it a good measure of spread for skewed distributions. It is obtained by evaluating $\frac{{Q}_{3}-{Q}_{1}}{2}$.

The mid-quartile range is the numerical value midway between the first and third quartile. It is one-half the sum of the first and third quartiles. It is obtained by evaluating $\frac{{Q}_{3}+{Q}_{1}}{2}$.

(The median, midrange and mid-quartile are not always the same value, although they may be.)